matrix inversion

[Hong Zhang]

On Fri, 21 Sep 2007, Randall Mackie wrote:

> I have a collegue who is considering to use PETSc for programming
> his problem. He would like to know if you can get the actual
> inverse of a matrix, because this inverse is embedded in another
> larger system that is then solved.

Then you may have to
- create a dense matrix Ainv
- call MatLUFactorSymbolic() and MatLUFactorNumeric() to get A=LU
- loop over matrix columns:
  MatSolve(LU,A(:,j),Ainv(:,j));
Note, if A is in row-compressed format, getting its columns is
VERY inefficient. Creating A as a dense matrix and using
Lapack or scalapack would give better result.
>
> I suppose that if you solve the system directly, say with SuperLU
> or MUMPS, you could get the actual inverse? I looked briefly through
> the manual and documentation, but it didn't jump out at me.

You get matrix factors: A = LU.
Then A*x = b is solved using MatSolve():
   L*y = b and U*x = y.

Again, sparse matrix A gives dense matrix inverse inv(A).
For computational efficiency and stability, we try to avoid
computing inv(A).

Hong


>
> Any advice here?
>
> Thanks, Randy
>
> --
> Randall Mackie
> GSY-USA, Inc.
> PMB# 643
> 2261 Market St.,
> San Francisco, CA 94114-1600
> Tel (415) 469-8649
> Fax (415) 469-5044
>
> California Registered Geophysicist
> License No. GP 1034
>
>